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In Escherichia coli, protein degradation in synthetic circuits is commonly achieved by the ssrA‐tagged degradation system. In this work, we show that the degradation kinetics for the green fluorescent protein fused with the native ssrA tag in each cell exhibits the zeroth‐order limit of the Michaelis–Menten kinetics, rather than the commonly assumed first‐order. When measured in a population, the wide distribution of protein levels in the cells distorts the true kinetics and results in a first‐order protein degradation kinetics as a population average. Using the synthetic gene‐metabolic oscillator constructed previously, we demonstrated theoretically that the zeroth‐order kinetics significantly enlarges the parameter space for oscillation and thus enhances the robustness of the design under parametric uncertainty.